We develop novel numerical methods for optimization problems subject to constraints given by nonlinear hyperbolic systems of conservation and balance laws in one space dimension. These types of control problems arise in a variety of applications,...

This thesis examines the Euler equations of gas dynamics and develops a new adaption indicator, which is based on the weak local residual measured for the non- conservative pressure variable. We demonstrate that the proposed indicator is capable of...

Flux gradient terms and source terms are two fundamental components of hyperbolic systems of balance law. Though having distinct mathematical natures, they form and maintain an exact balance in a special class of solutions, which are called...

A spatiotemporal system of partial differential equations is implemented for describing a marine predator-prey system of shark and prey fish. The model is developed to account for predator migration and for harvesting of both predator and prey...

This thesis is divided into two parts. In the first part (chapter 1, 2 and 3), we consider the semilinear elliptic equation$$\Delta u+k(x)u-f(x,u)=0\leqno(0.1)$$on a n-dimensional complete noncompact Riemannian manifold ($M,g$). In the special case...

he focus of this research has been devoted to study the interaction between two or more self-propelled toroidal swimmers in Stokes flow by applying the method of regularized Stokeslets and also study the effect of a nearby wall to the movement of a...

Explicit expressions for the location of trapped, and anti-trapped surfaces of cosmological origin in Friedmann type universes are obtained. Friedmann universes dominated by energy-momentum tensors of matter with an equation of state of the form $p...

Density functional theory (DFT) is a widely used quantum mechanical method for the simulation of the electronic structure of atoms, molecules, and solids. The only part that needs to be approximated is the exchange-correlation energy as a...

A numerical method for computing three-dimensional Stokes flow driven by a doubly-periodic array of regularized forces is presented. In the non-periodic direction either a free boundary or a homogeneous Dirichlet condition is enforced. The method...

An Honors Thesis Presented to The University Honors Program of Loyola University New Orleans In Partial Fulfillment of the Requirements for the Degree of Bachelor of Music in Music Education with University Honors